论文标题
在Kloosterman零的子空间和表格$ L_1（x^{ - 1}）+l_2（x）$的排列上
On subspaces of Kloosterman zeros and permutations of the form $L_1(x^{-1})+L_2(x)$
论文作者
论文摘要
形式$ f = l_1（x^{ - 1}）+L_2（x）$具有线性函数$ L_1，L_2 $的排列与几个有关CCZ等效性和逆函数的EA等值的有趣问题密切相关。在本文中，我们表明，如果$ l_1 $或$ l_2 $的内核太大，$ f $不能成为置换。证明的关键步骤是一个新的结果，即$ \ mathbb {f} _ {2^n} $的最大大小，仅包含Kloosterman Zeros，即一个子空间$ v $，因此$ k_n（v）= 0 $ in $ k_n（v）$ k_n（v）$ k_n（v）$ v）
Permutations of the form $F=L_1(x^{-1})+L_2(x)$ with linear functions $L_1,L_2$ are closely related to several interesting questions regarding CCZ-equivalence and EA-equivalence of the inverse function. In this paper, we show that $F$ cannot be a permutation if the kernel of $L_1$ or $L_2$ is too large. A key step of the proof is a new result on the maximal size of a subspace of $\mathbb{F}_{2^n}$ that contains only Kloosterman zeros, i.e. a subspace $V$ such that $K_n(v)=0$ for all $v \in V$ where $K_n(v)$ denotes the Kloosterman sum of $v$.}
